Gauge Dynamics and Topological Insulators

TL;DR

This paper explores how a non-abelian magnetic field in Yang-Mills theory creates a vortex lattice that leads to topologically protected Dirac points and the realization of a Z2 topological insulator in 2+1 dimensions.

Contribution

It demonstrates the formation of a vortex lattice and the emergence of topologically protected states, connecting gauge theory with topological insulator physics.

Findings

Identification of four topologically protected Dirac points.

Calculation of topological invariants showing Z2 topological insulator phase.

Evidence of topological phases arising from non-abelian gauge fields.

Abstract

A non-abelian magnetic field in Yang-Mills theory induces the formation of a "W-boson" vortex lattice. We study the propagation of fundamental fermions in the presence of this lattice in 2+1 dimensions. We show that the spectrum for massless fermions contains four topologically-protected Dirac points with non-zero Bloch momentum. For massive fermions, we compute topological invariants of the band structure and show that it is possible to realise a Z2 topological insulator within Yang-Mills theory.